%------------------------------------------------------------------------------
% File : E---3.5.1
% Problem : ITP101^1 : TPTP v9.3.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:04:21 AM UTC 2026
% Result : Theorem 0.20s 0.35s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 3
% Syntax : Number of formulae : 13 ( 8 unt; 0 typ; 0 def)
% Number of atoms : 45 ( 19 equ; 0 cnn)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 224 ( 17 ~; 11 |; 9 &; 175 @)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 5 ( 0 ^; 5 !; 0 ?; 5 :)
% Comments :
%------------------------------------------------------------------------------
thf(decl_sort1,type,
nat: $tType ).
thf(decl_sort2,type,
a: $tType ).
thf(decl_sort3,type,
list_a: $tType ).
thf(decl_23,type,
minus_minus_nat: nat > nat > nat ).
thf(decl_44,type,
nth_a: list_a > nat > a ).
thf(decl_46,type,
size_size_list_a: list_a > nat ).
thf(decl_47,type,
ord_less_nat: nat > nat > $o ).
thf(decl_53,type,
f: nat > a ).
thf(decl_54,type,
g: nat > a ).
thf(decl_55,type,
x: nat ).
thf(decl_56,type,
xs: list_a ).
thf(decl_57,type,
ys: list_a ).
thf(conj_3,conjecture,
( ( nth_a @ xs @ x )
= ( nth_a @ ys @ x ) ),
file('/export/starexec/sandbox/tmp/tmp.IvvJ2uKW2N/E---3.1_560537.p',conj_3) ).
thf(conj_1,hypothesis,
! [X156: nat] :
( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X156 )
= ( nth_a @ ys @ X156 ) ) )
& ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
= ( nth_a @ ys @ X156 ) ) ) ) )
& ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X156 )
= ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) )
& ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.IvvJ2uKW2N/E---3.1_560537.p',conj_1) ).
thf(conj_2,hypothesis,
ord_less_nat @ x @ ( size_size_list_a @ ys ),
file('/export/starexec/sandbox/tmp/tmp.IvvJ2uKW2N/E---3.1_560537.p',conj_2) ).
thf(c_0_3,negated_conjecture,
( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) ),
inference(assume_negation,[status(cth)],[conj_3]) ).
thf(c_0_4,hypothesis,
! [X156: nat] :
( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X156 )
= ( nth_a @ ys @ X156 ) ) )
& ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
= ( nth_a @ ys @ X156 ) ) ) ) )
& ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( nth_a @ xs @ X156 )
= ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) )
& ( ~ ( ord_less_nat @ X156 @ ( size_size_list_a @ ys ) )
=> ( ( f @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X156 @ ( size_size_list_a @ ys ) ) ) ) ) ) ) ),
inference(fof_simplification,[status(thm)],[conj_1]) ).
thf(c_0_5,negated_conjecture,
( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) ),
inference(fof_simplification,[status(thm)],[c_0_3]) ).
thf(c_0_6,hypothesis,
! [X1998: nat] :
( ( ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
| ( ( nth_a @ xs @ X1998 )
= ( nth_a @ ys @ X1998 ) )
| ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) )
& ( ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
| ( ( f @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ xs ) ) )
= ( nth_a @ ys @ X1998 ) )
| ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) )
& ( ~ ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
| ( ( nth_a @ xs @ X1998 )
= ( g @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ ys ) ) ) )
| ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) )
& ( ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) )
| ( ( f @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ xs ) ) )
= ( g @ ( minus_minus_nat @ X1998 @ ( size_size_list_a @ ys ) ) ) )
| ( ord_less_nat @ X1998 @ ( size_size_list_a @ ys ) ) ) ),
inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])])]) ).
thf(c_0_7,negated_conjecture,
( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) ),
inference(fof_nnf,[status(thm)],[c_0_5]) ).
thf(c_0_8,hypothesis,
! [X3: nat] :
( ( ( nth_a @ xs @ X3 )
= ( nth_a @ ys @ X3 ) )
| ~ ( ord_less_nat @ X3 @ ( size_size_list_a @ ys ) )
| ~ ( ord_less_nat @ X3 @ ( size_size_list_a @ ys ) ) ),
inference(split_conjunct,[status(thm)],[c_0_6]) ).
thf(c_0_9,negated_conjecture,
( ( nth_a @ xs @ x )
!= ( nth_a @ ys @ x ) ),
inference(split_conjunct,[status(thm)],[c_0_7]) ).
thf(c_0_10,hypothesis,
! [X3: nat] :
( ( ( nth_a @ ys @ X3 )
= ( nth_a @ xs @ X3 ) )
| ~ ( ord_less_nat @ X3 @ ( size_size_list_a @ ys ) ) ),
inference(cn,[status(thm)],[c_0_8]) ).
thf(c_0_11,hypothesis,
ord_less_nat @ x @ ( size_size_list_a @ ys ),
inference(split_conjunct,[status(thm)],[conj_2]) ).
thf(c_0_12,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : ITP101^1 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.05 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.18 % Computer : n011.cluster.edu
% 0.07/0.18 % Model : x86_64 x86_64
% 0.07/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.18 % Memory : 8046.5625MB
% 0.07/0.18 % OS : Linux 6.8.0-71-generic
% 0.07/0.18 % CPULimit : 300
% 0.07/0.18 % WCLimit : 300
% 0.07/0.18 % DateTime : Tue Sep 29 19:53:46 UTC 2026
% 0.07/0.18 % CPUTime :
% 0.07/0.18 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.07/0.23 Running higher-order theorem proving
% 0.20/0.27 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=300 /export/starexec/sandbox/tmp/tmp.IvvJ2uKW2N/E---3.1_560537.p
% 0.20/0.35 % Version: 3.5.1-ho
% 0.20/0.35 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.20/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.35 % Starting new_ho_10_unif with 300s (1) cores
% 0.20/0.35 % Starting sh10 with 300s (1) cores
% 0.20/0.35 % Starting lpo5_rw_fix with 300s (1) cores
% 0.20/0.35 % new_ho_10 with pid 560550 completed with status 0
% 0.20/0.35 % Result found by new_ho_10
% 0.20/0.35 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.20/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.35 % No SInE strategy applied
% 0.20/0.35 % Search class: HGHSM-FSLF32-MHFFFSBC
% 0.20/0.35 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 0.20/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.35 % Starting new_ho_10 with 151s (1) cores
% 0.20/0.35 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.20/0.35 % Starting new_ho_3 with 136s (1) cores
% 0.20/0.35 % Starting sh3 with 136s (1) cores
% 0.20/0.35 % lpo6_lambda_fix with pid 560559 completed with status 0
% 0.20/0.35 % Result found by lpo6_lambda_fix
% 0.20/0.35 % Preprocessing class: HSLSSMSSSSSNHFA.
% 0.20/0.35 % Scheduled 4 strats onto 8 cores with 300 seconds (2400 total)
% 0.20/0.35 % Starting new_ho_10 with 1500s (5) cores
% 0.20/0.35 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto)
% 0.20/0.35 % No SInE strategy applied
% 0.20/0.35 % Search class: HGHSM-FSLF32-MHFFFSBC
% 0.20/0.35 % partial match(1): HGHSM-FSLM32-MHFFFSBC
% 0.20/0.35 % Scheduled 7 strats onto 5 cores with 1500 seconds (1500 total)
% 0.20/0.35 % Starting SubtermCWHack with 136s (1) cores
% 0.20/0.35 % Starting new_ho_10 with 151s (1) cores
% 0.20/0.35 % Starting lpo6_lambda_fix with 136s (1) cores
% 0.20/0.35 % Preprocessing time : 0.015 s
% 0.20/0.35
% 0.20/0.35 % Proof found!
% 0.20/0.35 % SZS status Theorem
% 0.20/0.35 % SZS output start CNFRefutation
% See solution above
% 0.20/0.36 % Parsed axioms : 308
% 0.20/0.36 % Removed by relevancy pruning/SinE : 0
% 0.20/0.36 % Initial clauses : 710
% 0.20/0.36 % Removed in clause preprocessing : 74
% 0.20/0.36 % Initial clauses in saturation : 636
% 0.20/0.36 % Processed clauses : 34
% 0.20/0.36 % ...of these trivial : 2
% 0.20/0.36 % ...subsumed : 3
% 0.20/0.36 % ...remaining for further processing : 29
% 0.20/0.36 % Other redundant clauses eliminated : 16
% 0.20/0.36 % Clauses deleted for lack of memory : 0
% 0.20/0.36 % Backward-subsumed : 0
% 0.20/0.36 % Backward-rewritten : 0
% 0.20/0.36 % Generated clauses : 17
% 0.20/0.36 % ...of the previous two non-redundant : 16
% 0.20/0.36 % ...aggressively subsumed : 0
% 0.20/0.36 % Contextual simplify-reflections : 0
% 0.20/0.36 % Paramodulations : 1
% 0.20/0.36 % Factorizations : 0
% 0.20/0.36 % NegExts : 0
% 0.20/0.36 % Equation resolutions : 16
% 0.20/0.36 % Disequality decompositions : 0
% 0.20/0.36 % Total rewrite steps : 3
% 0.20/0.36 % ...of those cached : 1
% 0.20/0.36 % Propositional unsat checks : 0
% 0.20/0.36 % Propositional check models : 0
% 0.20/0.36 % Propositional check unsatisfiable : 0
% 0.20/0.36 % Propositional clauses : 0
% 0.20/0.36 % Propositional clauses after purity: 0
% 0.20/0.36 % Propositional unsat core size : 0
% 0.20/0.36 % Propositional preprocessing time : 0.000
% 0.20/0.36 % Propositional encoding time : 0.000
% 0.20/0.36 % Propositional solver time : 0.000
% 0.20/0.36 % Success case prop preproc time : 0.000
% 0.20/0.36 % Success case prop encoding time : 0.000
% 0.20/0.36 % Success case prop solver time : 0.000
% 0.20/0.36 % Current number of processed clauses : 13
% 0.20/0.36 % Positive orientable unit clauses : 8
% 0.20/0.36 % Positive unorientable unit clauses: 0
% 0.20/0.36 % Negative unit clauses : 2
% 0.20/0.36 % Non-unit-clauses : 3
% 0.20/0.36 % Current number of unprocessed clauses: 618
% 0.20/0.36 % ...number of literals in the above : 2415
% 0.20/0.36 % Current number of archived formulas : 0
% 0.20/0.36 % Current number of archived clauses : 0
% 0.20/0.36 % Clause-clause subsumption calls (NU) : 1
% 0.20/0.36 % Rec. Clause-clause subsumption calls : 1
% 0.20/0.36 % Non-unit clause-clause subsumptions : 0
% 0.20/0.36 % Unit Clause-clause subsumption calls : 0
% 0.20/0.36 % Rewrite failures with RHS unbound : 0
% 0.20/0.36 % BW rewrite match attempts : 0
% 0.20/0.36 % BW rewrite match successes : 0
% 0.20/0.36 % Condensation attempts : 34
% 0.20/0.36 % Condensation successes : 0
% 0.20/0.36 % Termbank termtop insertions : 58456
% 0.20/0.36 % Search garbage collected termcells : 12828
% 0.20/0.36
% 0.20/0.36 % -------------------------------------------------
% 0.20/0.36 % User time : 0.053 s
% 0.20/0.36 % System time : 0.011 s
% 0.20/0.36 % Total time : 0.064 s
% 0.20/0.36 % Maximum resident set size: 6476 pages
% 0.20/0.36
% 0.20/0.36 % -------------------------------------------------
% 0.20/0.36 % User time : 0.107 s
% 0.20/0.36 % System time : 0.031 s
% 0.20/0.36 % Total time : 0.139 s
% 0.20/0.36 % Maximum resident set size: 5376 pages
% 0.20/0.36 % E exiting
%------------------------------------------------------------------------------